91Ó°ÊÓ

Trigonometric Form of a Complex Number \(\mathrm{In}\) Exercises \(11-30\) , represent the complex number graphically. Then write the trigonometric form of the number. $$-2(1+\sqrt{3} i)$$

Using the Law of Sines. Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=55^{\circ}, \quad B=42^{\circ}, \quad c=\frac{3}{4}$$

Using the Law of Cosines, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$ a=75.4, \quad b=52, \quad c=52 $$

Trigonometric Form of a Complex Number \(\mathrm{In}\) Exercises \(11-30\) , represent the complex number graphically. Then write the trigonometric form of the number. $$\frac{5}{2}(\sqrt{3}-i)$$

Using the Law of Cosines, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$ a=1.42, \quad b=0.75, \quad c=1.25 $$

In Exercises \(15-24,\) use the vectors \(u=\langle 3,3\rangle, \quad v=\langle- 4,2\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$3 \mathbf{u} \cdot \mathbf{v}$$

Using the Law of Sines. Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$B=28^{\circ}, \quad C=104^{\circ}, \quad a=3 \frac{5}{8}$$

Using the Law of Cosines, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$ A=120^{\circ}, \quad b=6, \quad c=7 $$

In Exercises \(15-24,\) use the vectors \(u=\langle 3,3\rangle, \quad v=\langle- 4,2\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$(\mathbf{u} \cdot \mathbf{v}) \mathbf{v}$$

Using the Law of Sines. Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=36^{\circ}, \quad a=8, \quad b=5$$